Low energy excitations of the t-J model in 1D and 2D

TL;DR

This study uses exact diagonalization to analyze low energy excitations in 1D and 2D t-J models, revealing linear energy dependence on parameters and collective modes related to hole density modulations.

Contribution

It provides a detailed characterization of low energy states in the t-J model, highlighting the linear energy relation and collective excitations in 2D.

Findings

Energy levels follow E(t,J) = a t + b J in most low energy states.

In 2D, the lowest singlet states are collective modes with hole density modulations.

Hole behavior can be modeled as hard-core Bosons with attractive interactions.

Abstract

We present an exact diagonalization study of the low energy singlet and triplet states for both 1D and 2D t-J model. A scan of the parameter ratio J/t shows that for nearly all low energy states in both 1D and 2D the excitation energy takes the linear form E(t,J) = a t + b J. In 1D this is the natural consequence of the factorization of the low energy wave functions, i.e. spin-charge separation. Examination of the low energy eigenstates in 2D shows that in the singlet sector the lowest states are collective modes, which for larger J correspond to `dynamical hole columns', i.e. a periodic modulation of the hole density. This modulation is well reproduced by treating holes as hard-core Bosons with an attractive interaction.